Purpose Magnetohydrodynamic (MHD) flows are widely applied in electromagnetic casting, magnetic drug targeting, plasma confinement and nuclear reactor cooling. The model can be used in microelectronic heat management, electromagnetic cooling, and aircraft thermal systems. The purpose of this study is to analyze the momentum and heat transport characteristics of a two-phase dusty nanofluid flowing over a curved Riga surface under the modified Fourier (Cattaneo–Christov) heat flux model. Methodology The governing equations are converted into ordinary differential equations by similarity transformations after being created with suitable boundary conditions. Using the bvp4c method, numerical results are obtained. An artificial neural network (ANN) based on the Backpropagated Levenberg–Marquardt method and Bayesian Regularisation is created using the collected numerical data in order to envisage flow behaviour under several physical factors. Results The flow is greatly restricted by the suspension of dust particles of uniform size, leading to decrease in heat transfer rate and reduction in velocity, depending on the curvature and magnetic field parameters. While decreasing the velocity of dust-phase, increasing the curvature parameter increases the velocity of fluid-phase. Originality and conclusion The originality of this work lies in integrating a dusty two-phase model, a curved Riga surface, and an ANN-based predictive framework under the modified Fourier law. This work is novel because it combines an ANN approach with a dusty two-phase Riga curved flow and the Modified Fourier heat flux model. The results demonstrate that dust loading and surface curvature strongly influence MHD flow behavior, while LM modeling provides an efficient and accurate alternative to traditional numerical approaches. The findings demonstrate that while Bayesian Regularisation outperforms the Levenberg–Marquardt algorithm in terms of prediction accuracy, the adjusted Hartmann parameter decreases velocity. For complicated nonlinear thermal-fluid transport phenomena, the suggested methodology offers both intelligent and numerical predictive analysis.